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Tr. Mat. Inst. Steklova, 1999, Volume 226, Pages 163–179 (Mi tm536)  

This article is cited in 19 scientific papers (total in 19 papers)

Quantum Mapping Class Group, Pentagon Relation, and Geodesics

V. V. Focka, L. O. Chekhovb

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The mapping class group transformations that satisfy the pentagon relation are constructed for classical and quantum Teichmüller spaces coordinatized in terms of graphs. Classical and quantum geodesic algebras governed by the skein relations are discussed.

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English version:
Proceedings of the Steklov Institute of Mathematics, 1999, 226, 149–163

Bibliographic databases:

Document Type: Article
UDC: 530.1
Received in April 1999

Citation: V. V. Fock, L. O. Chekhov, “Quantum Mapping Class Group, Pentagon Relation, and Geodesics”, Mathematical physics. Problems of quantum field theory, Collection of papers dedicated to the 65th anniversary of academician Lyudvig Dmitrievich Faddeev, Tr. Mat. Inst. Steklova, 226, Nauka, MAIK Nauka/Inteperiodika, M., 1999, 163–179; Proc. Steklov Inst. Math., 226 (1999), 149–163

Citation in format AMSBIB
\Bibitem{FocChe99}
\by V.~V.~Fock, L.~O.~Chekhov
\paper Quantum Mapping Class Group, Pentagon Relation, and Geodesics
\inbook Mathematical physics. Problems of quantum field theory
\bookinfo Collection of papers dedicated to the 65th anniversary of academician Lyudvig Dmitrievich Faddeev
\serial Tr. Mat. Inst. Steklova
\yr 1999
\vol 226
\pages 163--179
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm536}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782560}
\zmath{https://zbmath.org/?q=an:0983.32021}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1999
\vol 226
\pages 149--163


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. O. Chekhov, “A spectral problem on graphs and $L$-functions”, Russian Math. Surveys, 54:6 (1999), 1197–1232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. R. M. Kashaev, “Liouville Central Charge in Quantum Teichmüller Theory”, Proc. Steklov Inst. Math., 226 (1999), 63–71  mathnet  mathscinet  zmath
    3. Chekhov L.O., Fock V.V., “Observables in 3D gravity and geodesic algebras”, Czechoslovak Journal of Physics, 50:11 (2000), 1201–1208  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Faddeev L., “Modular double of a quantum group”, Conference Moshe Flato 1999, Mathematical Physics Studies, 21, 2000, 149–156  mathscinet  zmath  isi
    5. L. O. Chekhov, “Observables in $2+1$ Gravity and Noncommutative Teichmüller Spaces”, Theoret. and Math. Phys., 129:2 (2001), 1609–1616  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. L. O. Chekhov, R. C. Penner, “Introduction to quantum Thurston theory”, Russian Math. Surveys, 58:6 (2003), 1141–1183  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Faddeev L.D., “Discretized Virasoro algebra”, Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemporary Mathematics Series, 391, 2005, 59–67  crossref  mathscinet  zmath  isi
    8. Chekhov L., Nelson J.E., Regge T., “Extension of geodesic algebras to continuous genus”, Letters in Mathematical Physics, 78:1 (2006), 17–26  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. G. B. Shabat, V. I. Zolotarskaya, “The Chekhov–Fock parametrization of Teichmüller spaces and dessins d'enfants”, J. Math. Sci., 158:1 (2009), 155–161  mathnet  crossref  mathscinet  elib  elib
    10. L. O. Chekhov, “Riemann Surfaces with Orbifold Points”, Proc. Steklov Inst. Math., 266 (2009), 228–250  mathnet  crossref  mathscinet  zmath  isi
    11. M. Mazzocco, L. O. Chekhov, “Orbifold Riemann surfaces: Teichmüller spaces and algebras of geodesic functions”, Russian Math. Surveys, 64:6 (2009), 1079–1130  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Chekhov L.O., “Orbifold Riemann surfaces and geodesic algebras”, Journal of Physics A–Mathematical and Theoretical, 42:30 (2009), 304007  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Nelson J.E., Picken R.F., “A Quantum Goldman Bracket for Loops on Surfaces”, International Journal of Modern Physics A, 24:15 (2009), 2839–2856  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. Chekhov L., Mazzocco M., “Isomonodromic deformations and twisted Yangians arising in Teichmüller theory”, Adv Math, 226:6 (2011), 4731–4775  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    15. Chekhov L., Mazzocco M., “Teichmüller Spaces as Degenerated Symplectic Leaves in Dubrovin-Ugaglia Poisson Manifolds”, Physica D, 241:23-24 (2012), 2109–2121  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    16. Chekhov L., Shapiro M., “Teichmüller Spaces of Riemann Surfaces with Orbifold Points of Arbitrary Order and Cluster Variables”, Int. Math. Res. Notices, 2014, no. 10, 2746–2772  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    17. Teschner J., Vartanov G.S., “Supersymmetric Gauge Theories, Quantization of M-Flat, and Conformal Field Theory”, Adv. Theor. Math. Phys., 19:1 (2015), 1–135  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. Chekhov L.O., Mazzocco M., Rubtsov V.N., “Painlevé Monodromy Manifolds, Decorated Character Varieties, and Cluster Algebras”, Int. Math. Res. Notices, 2017, no. 24, 7639–7691  crossref  mathscinet  isi
    19. Chekhov L., Mazzocco M., “Colliding Holes in Riemann Surfaces and Quantum Cluster Algebras”, Nonlinearity, 31:1 (2018), 54–107  crossref  mathscinet  zmath  isi  scopus  scopus
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